3.1224 \(\int (1-2 x)^2 (2+3 x)^3 (3+5 x) \, dx\)

Optimal. Leaf size=45 \[ \frac{20}{567} (3 x+2)^7-\frac{8}{27} (3 x+2)^6+\frac{91}{135} (3 x+2)^5-\frac{49}{324} (3 x+2)^4 \]

[Out]

(-49*(2 + 3*x)^4)/324 + (91*(2 + 3*x)^5)/135 - (8*(2 + 3*x)^6)/27 + (20*(2 + 3*x
)^7)/567

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Rubi [A]  time = 0.0650513, antiderivative size = 45, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ \frac{20}{567} (3 x+2)^7-\frac{8}{27} (3 x+2)^6+\frac{91}{135} (3 x+2)^5-\frac{49}{324} (3 x+2)^4 \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)^2*(2 + 3*x)^3*(3 + 5*x),x]

[Out]

(-49*(2 + 3*x)^4)/324 + (91*(2 + 3*x)^5)/135 - (8*(2 + 3*x)^6)/27 + (20*(2 + 3*x
)^7)/567

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{540 x^{7}}{7} + 144 x^{6} + \frac{99 x^{5}}{5} - \frac{425 x^{4}}{4} - \frac{154 x^{3}}{3} + 24 x + 52 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)**2*(2+3*x)**3*(3+5*x),x)

[Out]

540*x**7/7 + 144*x**6 + 99*x**5/5 - 425*x**4/4 - 154*x**3/3 + 24*x + 52*Integral
(x, x)

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Mathematica [A]  time = 0.00176407, size = 42, normalized size = 0.93 \[ \frac{540 x^7}{7}+144 x^6+\frac{99 x^5}{5}-\frac{425 x^4}{4}-\frac{154 x^3}{3}+26 x^2+24 x \]

Antiderivative was successfully verified.

[In]  Integrate[(1 - 2*x)^2*(2 + 3*x)^3*(3 + 5*x),x]

[Out]

24*x + 26*x^2 - (154*x^3)/3 - (425*x^4)/4 + (99*x^5)/5 + 144*x^6 + (540*x^7)/7

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Maple [A]  time = 0.001, size = 35, normalized size = 0.8 \[{\frac{540\,{x}^{7}}{7}}+144\,{x}^{6}+{\frac{99\,{x}^{5}}{5}}-{\frac{425\,{x}^{4}}{4}}-{\frac{154\,{x}^{3}}{3}}+26\,{x}^{2}+24\,x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^2*(2+3*x)^3*(3+5*x),x)

[Out]

540/7*x^7+144*x^6+99/5*x^5-425/4*x^4-154/3*x^3+26*x^2+24*x

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Maxima [A]  time = 1.3452, size = 46, normalized size = 1.02 \[ \frac{540}{7} \, x^{7} + 144 \, x^{6} + \frac{99}{5} \, x^{5} - \frac{425}{4} \, x^{4} - \frac{154}{3} \, x^{3} + 26 \, x^{2} + 24 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)*(3*x + 2)^3*(2*x - 1)^2,x, algorithm="maxima")

[Out]

540/7*x^7 + 144*x^6 + 99/5*x^5 - 425/4*x^4 - 154/3*x^3 + 26*x^2 + 24*x

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Fricas [A]  time = 0.182489, size = 1, normalized size = 0.02 \[ \frac{540}{7} x^{7} + 144 x^{6} + \frac{99}{5} x^{5} - \frac{425}{4} x^{4} - \frac{154}{3} x^{3} + 26 x^{2} + 24 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)*(3*x + 2)^3*(2*x - 1)^2,x, algorithm="fricas")

[Out]

540/7*x^7 + 144*x^6 + 99/5*x^5 - 425/4*x^4 - 154/3*x^3 + 26*x^2 + 24*x

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Sympy [A]  time = 0.082697, size = 39, normalized size = 0.87 \[ \frac{540 x^{7}}{7} + 144 x^{6} + \frac{99 x^{5}}{5} - \frac{425 x^{4}}{4} - \frac{154 x^{3}}{3} + 26 x^{2} + 24 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**2*(2+3*x)**3*(3+5*x),x)

[Out]

540*x**7/7 + 144*x**6 + 99*x**5/5 - 425*x**4/4 - 154*x**3/3 + 26*x**2 + 24*x

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GIAC/XCAS [A]  time = 0.204147, size = 46, normalized size = 1.02 \[ \frac{540}{7} \, x^{7} + 144 \, x^{6} + \frac{99}{5} \, x^{5} - \frac{425}{4} \, x^{4} - \frac{154}{3} \, x^{3} + 26 \, x^{2} + 24 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)*(3*x + 2)^3*(2*x - 1)^2,x, algorithm="giac")

[Out]

540/7*x^7 + 144*x^6 + 99/5*x^5 - 425/4*x^4 - 154/3*x^3 + 26*x^2 + 24*x